Question

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class sze of each. The results are shown in the table below. At α 0.01, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 32 32 31 36 29 28 42 26 26C 29 29 28 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and Ha? o-B, Ho: μ > 32 OA. Ηοιμ 32 Ha : μ#32 Ha : μ s 32 Ha : μ<32 OE. Ho : μ < 32 Ha : μ<32 Ha:p232 Ha H>32 (b) Use technology to find the P-value. P(Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? A. Fail to reject H0 because the P-value is less than the sagnificance level. ( O B. Reject Ho because the P-value is less than the significance level.

Answer 1

a) The null and alternative hypotheses are,

Ho : μ=32

Ha : μ < 32

b) Using TI-84 calculator we get,

Test statistic = t = -1.690

p-value = p = 0.055

c) p = 0.055 > 0.01

=> Fail to reject H₀ because the P-value is greater than the significance level.

d) At the 1% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 32 students.

TI-84 Plus TEXAS INSTRUMENTS T-Test μ<32 t--1. 699279522 P-1 05461J2066 43283 05555556 SpF4-88060052 n=18 STAT PLOTF1 TBLSET F2 FORMAT F3 ALC F4 TABLE F INDO QUIT INS 2ND MODE DEL A-LOCK LINK LIST ALPHA X,T,θ,n STAT TEST A ANGLE B DRAW c MATH CLEAR APPS VARS PRGM MATRIX D SINE cos' F x녔 SIN TAN COS e M 10* N w Q V P LOG 7 9 8 e* s L4 T LN LG V L5 U 4 6 RCL X 5 MEM " STO L1 Y L2 Z ENTRY SOLVE OFF 3 2 ENTER ON CATALOG ANS ? 0